White House hopeful Donald Trump says he is unlikely to have a good relationship with British Prime Minister David Cameron and has suggested London’s new Muslim mayor, Sadiq Khan, is “ignorant” and should take an IQ test.

Republican nominee Trump has fought a war of words with British politicians since controversially calling for a ban on Muslims entering the US last year.

Reacting to calls to have Trump banned from the UK for the remarks, Cameron called the property tycoon’s proposal “divisive, stupid and wrong.”

"Of course we stand by what we said when he made it clear he didn't want Muslims coming into the United States.

"Both myself, David Cameron and others were pretty clear that was not a view we supported.

"But he's an American presidential candidate and we will talk to him because it is in our interests to talk to our allies like the United States of America."

Trump is expected to visit London this summer during a tour of foreign capitals in the run-up to the American election.

Meanwhile Trump, who had previously wished newly elected London Mayor Sadiq Khan well, says he is offended by Khan’s comments that he is ignorant about Islam.

“He doesn’t know me, never met me, doesn’t know what I am all about. I think they are very rude statements.

“Frankly tell him I will remember those statements. They are very nasty statements. It is ignorant for him to say that.

“When he won I wished him well. Now, I don’t care about him. I mean it doesn’t make any difference to me. Let’s see how he does, let’s see if he is a good mayor,” Trump said.

A spokesperson for Khan has hit back at the comments, saying: “Donald Trump’s views are ignorant, divisive and dangerous - it’s the politics of fear at its worst and will be rejected at the ballot box just as it was in London.”

Asked if Khan would take up an offer of an IQ test, the spokesperson said: “Ignorance is not the same as a lack of intelligence.”